Cellular Neuroscience 207 Ian Parker Lecture 1 Enough

Cellular Neuroscience (207) Ian Parker Lecture # 1 - Enough (but not too much!) electronics to call yourself a cellular neurophysiologist http: //parkerlab. bio. uci. edu

Ohm’s Law Current I battery V V (Volts) resistor R V = IR - electrical driving force (water pressure) [voltage, potential difference, p. d. are all synonyms] I (Amperes) - electrical current flow (gallons per minute) R (Ohms) - resistance R = V/I so, if V = 1 volt (how narrow the pipe is) for R = 1 W for R = 1 k W I = 1 A I = 10^-3 A (1 m. A)

Charge = amount of electricity (number of electrons : gallons of water) = current * time 1 A * 1 sec = 1 Coulomb (C) [How many electrons are there in a Coulomb? ? ]

Resistors in series and parallel I R 1 Total R = R 1 + R 2 I = V / (R 1 + R 2) V R 1 I = I 1 + I 2 R 2 I 2 1/ total R = 1/R + 1/ R 2

Conductance is the reciprocal of resistance (i. e. how easily something conducts electricity) Conductance (G) = 1/R Unit : Siemen (S) = 1/ 1 W total conductance G = G 1 + G 2 G 1 I = I 1 + I 2 G 2 I 2 From Ohms law I = V / R So I =V*G Itotal = V * (G 1 + G 2)

Voltage dividers E - V * R 2 /(R 1 + R 2) R 1 V R 2 E [ If V = 1 V, R 1 = 9 k. W and R 2 = 1 k. W what is E? : what current flows through R 1? ]

Capacitance Capacitor - two conductors separated by an insulating gap (dielectric) e. g. 2 metal plates separated by an air gap Capacitance (C) increases as; 1. The area of the plates is increased 2. The separation between the plates is decreased 3. The dielectric constant of the insulator is increased Capacitors store electricity, but cannot pass a steady current Unit : Farad (F) 1 F = capacitor that will store 1 Coulomb when connected to 1 V Charge (q) stored on a capacitor = C * V

RC (resistor/capacitor) circuits 1. Low-pass RC circuit switch V R E C Voltage rises exponentially from zero to V with time constant t t is time for change to 1/e of final voltage ( e = 2. 71828…) t (sec) = R (W) * C (F) Switch closed [what is t if R = 1 MW, C = 1 m. F? ]

The effect of a low-pass circuit is to pass steady or slowly changing signals while filtering out rapidly changing signals brief change in voltage longer change in voltage

RC (resistor/capacitor circuits) 2. High-pass RC circuit switch C V E R Output voltage instantly rises to match input voltage, then decays exponentially. Time constant of decay t = RC Effect is to block rapidlychanging voltages (capacitor is an insulator), but pass rapidly changing signals

What does all this mean for a NEURON? The cell membrane (lipid bilayer) acts as a very good insulator, but has high capacitance. Specific membrane resistance 1 cm Resistance of 1 cm 2 of membrane (Rm) Rm of a lipid bilayer >106 W cm 2 But membrane channels can greatly increase the membrane conductance

Specific membrane capacitance extracellular fluid membrane intracellular fluid The insulating cell membrane (dielectric) separates two good conductors (the fluids outside and inside the cell), thus forming a capacitor. Because the membrane is so thin (ca. 7. 5 nm), the membrane acts as a very good capacitor. Specific capacitance (capacitance of 1 cm 2 of membrane : Cm) Cm ~ 1 m. F cm-2 for cell membranes

Input resistance of a cell Record voltage (V) Inject current (I) cell Input resistance Rin = V/I Rin decreases with increasing size of cell (increasing membrane area) Rin increases with increasing specific membrane resistance [If I = 10 n. A and V = 5 m. V, what is Rm ? ? ? ]

A neuron as an RC circuit Record voltage (V) Inject current (I) I cell inside Cm Rm outside Voltage changes exponentially with time constant tm

t m = Rm * C m So tm will be longer if Rm is high “ “ “ and if Cm is high We can directly measure Rm and tm so we can calculate Cm = tm / Rm Given that Cm ~ 1 m. F cm 2, we can then calculate the membrane area of the cell